Annals of Glaciology 50 2009
135
The influence of drainage boundaries on specific mass-balance
results: a case study of Engabreen, Norway
Hallgeir ELVEHØY, Miriam JACKSON, Liss M. ANDREASSEN
Norwegian Water Resources and Energy Directorate (NVE), Middelthunsgate 29, PO Box 5091, Majorstua,
NO-0301 Oslo, Norway
E-mail: [email protected]
ABSTRACT. Mass-balance measurements were initiated on Engabreen, an outlet glacier from the
Svartisen ice cap, Norway, in 1970. The glacier boundary was defined based on where meltwater
drained, as the interest in Engabreen was mainly hydrological. However, the apparent discrepancy
between the calculated cumulative glacier mass balance since 1970 and changes in glacier geometry
prompted a re-examination of the glacier boundary. The glaciological drainage boundary is defined by
studying whether ice flow physically contributes to Engabreen tongue and corresponds to a glacier with
an area of 27.2 km2, significantly smaller than that defined by the hydrological drainage boundary at
39.6 km2. This glaciological drainage boundary is here named the ice-flow perimeter. The area
difference between this and the hydrological drainage boundary is largest for the altitudinal range 1300–
1400 m a.s.l. Generally, the ‘glaciological’ glacier is lower in mean altitude than the ‘hydrological’
glacier, and this affects the calculated specific mass balance. Using the glaciological boundary leads to
reductions in mean annual winter and summer balance (when spatial differences are ignored) of
0.12 m w.e. (from 2.92 to 2.80 m w.e.) and 0.15 m w.e. (from –2.32 to –2.47 m w.e.), respectively. The
reduction in mean net balance for the period 1970–2006 is 0.27 m w.e. (from +0.59 to +0.32 m w.e.)
which is about 50% of the calculated mass surplus in this period. This illustrates that the choice of
glacier outline can significantly influence the long-term cumulative mass balance and that results from
outlet glaciers must be interpreted with care when used for regional estimates of glacier change.
INTRODUCTION
Glacier mass-balance data are used to estimate the contribution to sea-level change from melting glaciers (e.g. Zuo
and Oerlemans, 1997; Dyurgerov and Carter, 2004;
Oerlemans and others, 2005; Raper and Braithwaite,
2006). Glaciers are also sensitive indicators of climate
140change, and the cumulative mass-balance curves are
used to report on the development of glaciers in different
regions (e.g. Lemke and others, 2007; WGMS, 2007). The
estimates of glacier change and sea-level rise depend
heavily on the quality of measurements and calculations
for the few glaciers where there exists a long-term series of
mass-balance data. Glacier mass balance is monitored using
the direct glaciological method whereby the measurements
are extrapolated from point observations to the surface area
of the glacier or glacier basin. The long-term cumulative net
balance is sensitive to systematic errors which accumulate,
and thus influence the accuracy of estimates of glacier
changes and sea-level rise.
Mass-balance measurements in Norway have traditionally been related to the needs of hydropower development.
The primary interest was the effect of glaciers on run-off in
hydrological catchments. Hence, glacier boundaries were
often defined by catchments of downstream gauging
stations. Where the glacier bottom topography is known,
the hydrological drainage divides can be mapped by
calculating the hydraulic head. The glaciological drainage
divide, or ice-flow perimeter, defines the area draining ice to
glacier outlets and can deviate considerably from the
hydrological drainage divide, as illustrated in previous
studies of Blåmannsisen (Kennett, 1990) and western
Svartisen (Kennett and others, 1997). In Norway, 28 of the
42 glaciers where mass balance has been measured are
outlets from plateau glaciers. In 2007, 10 out of 13
measured glaciers were outlet glaciers (Kjøllmoen, 2008).
Engabreen is an outlet glacier from western Svartisen ice
cap, northern Norway. Mass-balance measurements were
initiated on the glacier in 1970 in association with a planned
hydropower scheme in the area. The glacier has the only
long term mass-balance series in northern Norway, and the
series has been used in several studies (e.g. Engeset and
others, 2000; Rasmussen and Conway, 2005; Schuler and
others, 2005). Engabreen is also one of 30 reference glaciers
with long-term uninterrupted measurements used by the
World Glacier Monitoring Service (WGMS) for calculating
mean specific balances (WGMS, 2007).
Here we investigate the influence on area-averaged massbalance results from three different glacier boundaries for
Engabreen: ice drainage to a hydrological gauging station
based on surface topography; subglacial water drainage to a
hydrological gauging station based on glacier bed topography and ice thickness; and ice drainage to the glacier
tongue based on ice movement and surface topography. The
objectives are to study the impact of different drainage
divides on the area-to-altitude distribution and the implications on the long-term mass-balance record.
SETTING
Engabreen (668400 N, 138500 E) is a northern outlet glacier
from the western Svartisen ice cap (221 km2) in Nordland,
northern Norway. It is located in a mountainous area close
to the ocean, with peaks at 1400–1600 m a.s.l. Engabreen
covers about 39 km2 (depending on how the boundaries are
defined) and ranges in altitude from 10 m a.s.l. (in 2001) to
136
Elvehøy and others: Drainage boundaries and mass-balance results
tions for Engabreen were made using this map until 2003.
Four high-quality DEMs were constructed from laser
scanning measurements in the period 2001–03, and their
vertical accuracy is better than 0.3 m (Geist and others,
2005). The DEM from 24 September 2001 has been used for
mass-balance calculations since 2004. The glacier margin
was drawn manually from terrain shape in this DEM, as the
glacier outline is better defined in September due to less
snow at the glacier margin, but this DEM was incomplete at
the glacier tongue. Hence, a DEM from 30 June 2003 is used
to calculate the altitudinal distributions.
Fig. 1. Location map of Engabreen and Storglombreen, the major
outlets from western Svartisen. Glacier areas are light grey. The
global positioning system base Holandsfjord is shown (triangle).
1575 m a.s.l. (Figs 1 and 2). Below 900 m a.s.l., there is a
heavily crevassed icefall which accounts for 7% of the
glacier area. The glacier tongue is exposed to periodic
melting throughout the winter due to the frequent occurrence of positive temperatures at sea level in a maritime
climate. The distance along a flowline from the ice divide
west of Snøtind to the glacier terminus is 11 km. The average
slope on the plateau above 900 m a.s.l. is 48, while the mean
slope of the icefall is 158.
DATA
Mass-balance data
Glacier mass-balance observations at Engabreen began in
1970. The mass-balance data are published annually or
biannually in the Norwegian Water Resources and Energy
Directorate (NVE) report series (e.g. Kjøllmoen, 2008). The
data from Engabreen are also reported to the WGMS and
published in its Glacier Mass Balance Bulletin series (e.g.
WGMS, 2007).
The mass balance is measured by the direct glaciological
method (Østrem and Brugman, 1991). The extent of the
measurements has varied considerably over time. A total of
20–30 stake locations were used between 1970 and 1982,
and snow depth was sounded at 200–400 points on the
glacier plateau. Snow density was measured at one to three
locations. Mass balance is presently measured at five to ten
stake locations, snow depth is measured at approximately
50 points, and the snow density is measured at one location.
The mass balance is calculated using a stratigraphic method,
i.e. between two successive ‘summer surfaces’ (surface
minima). Between 1970 and 1988 the mass balance was
calculated using the balance-map method, while the
balance vs altitude method has been used since 1989. The
mass-balance methods and calculations are described in
further detail by Andreassen and others (2005) and
Kjøllmoen (2008). Average specific winter and summer
mass balance are 2.92 and –2.32 m w.e. The assumed
uncertainty in annual specific net balance is 0.3 m w.e.,
and the corresponding uncertainty for 37 years of cumulative net balance is 2 m w.e. (Andreassen and others,
2002, 2005).
Digital elevation models
Several digital elevation models (DEMs) exist for Engabreen.
The oldest is based on a map constructed from aerial
photography on 24 August 1968. The mass-balance calcula-
Bed topography
Bed topography on western Svartisen has been mapped
using ground-penetrating radar (GPR) from the glacier
surface (Sætrang, 1988). In addition, ice thickness has been
measured in the icefall of Engabreen using helicopter-borne
GPR (Kennett and others, 1993). A DEM of the bed
topography of western Svartisen was then calculated from
interpolated ice thickness and surface topography (Kennett
and others, 1997).
Drainage divides
Mass-balance measurements at Engabreen were initiated
with the primary purpose of investigating the influence of
glaciers on regional hydrology for hydroelectric power
planning. The investigated area included all glaciers in the
catchment to lake Engabrevatnet where river discharge was
measured, i.e. the two outlet glaciers Engabreen and
Litlebreen, and large areas on the plateau of Svartisen.
Without knowledge of the ice thickness or ice dynamics, the
catchment boundary on the glacier plateau was drawn
based on the surface topography from 1968, thereby
corresponding to an ice divide defined only by terrain slope
(Tvede and others, 1971). In the southeast basin close to
Snøtind, the divide was drawn parallel to the general surface
slope in the middle of the basin where the glacier is >400 m
thick. This ice drainage divide is shown in Figure 2.
When glacier run-off is assessed, a hydrological drainage
basin must be used. Glacier meltwater percolates through
the glacier and flows along the glacier bed driven by
gradients in hydraulic potential elevation. Based on glacier
bottom topography and ice thickness, the hydraulic head or
hydraulic potential elevation at Svartisen was mapped and
the drainage boundary to Engabrevatnet was defined
(Kennett and others, 1997). The boundaries based on surface
topography and hydraulic potential elevations are quite
similar, except in the southeast basin where the hydraulic
potential elevation boundary includes most of this basin
(Fig. 2).
METHODS
Velocity measurements
Previous studies of surface dynamics in the southeastern part
of Engabreen (e.g. Jackson and others, 2005) have suggested
that ice flow here may be towards the east rather than the
west, and hence the ice actually belongs glaciologically to
the glacier Storglombreen. To study this further, nine stakes
were installed in the region of the boundary between
Engabreen and Storglombreen in summer 2006 (Fig. 1).
Stakes were about 500 m apart and were thus all situated
within an area of 1 km2.
Elvehøy and others: Drainage boundaries and mass-balance results
Displacement was measured using the differential global
positioning system (dGPS) over a 98 day period in order to
determine the direction of ice flow. Measurements were
made on 28 June, 3 August and 4 October. The base station
for the GPS measurements in August and October was at
Holandsfjord (Fig. 1). The station at Holandsfjord is part of
the geodetic network of the Norwegian Mapping Authority,
and has an absolute accuracy of 3 cm horizontally and 5 cm
vertically. Holandsfjord is within 11 km of the stakes, so the
absolute accuracy of positions calculated using Holandsfjord is 5 cm. As the same base station was used for August
and October, the displacement and angle measured over this
period depend only on the relative accuracy, which is better
than 2 cm. For the measurements in June, some of the stake
positions were calculated using a base station at Bautaen
(Fig. 2) and others using the SATREF station at Bodø (SATREF
is a satellite-based reference system of the Norwegian
Mapping Authority and provides correction data for GPS
measurements made without a base station). Bautaen is
within 4 km of the stakes, so the absolute accuracy of
positions is within 11 cm. Positions calculated using the
SATREF station at Bodø at a distance of about 73 km have an
accuracy within 10 cm. Both speed and direction of surface
movement were approximately consistent for each measurement period (Table 1).
On the whole, the GPS measurements were made over a
long enough period, in terms both of the amount of time the
receiver collected satellite data and of the time between
position measurements, that the velocity data given are
assumed to be reliable in determining the direction of ice
flow as well as approximate magnitude. Some of the stakes
measured in October were either slanted or had melted out,
but their position was still easily distinguishable. This will
have incorporated an additional uncertainty into the October positions, but not more than 10 cm, and the magnitude
of errors is small compared with displacements.
Altitudinal area distribution
We made three glacier basins from the three different
drainage divides and the glacier outline from 24 September
2001. The DEM (5 m cell size) from 30 June 2003 was then
cut with the glacier basins, and the area–elevation distribution was calculated within 100 m elevation bins. The grid-
137
Fig. 2. Three different drainage basins for Engabreen: ice drainage
divide based on surface topography (light grey); hydrological
drainage divide (black line); and ice drainage based on measured
ice movement and surface topography (dark grey). Arrows with
letters show direction of movement from velocity measurements
from 2006 listed in Table 1.
node counting included all cells where the node point was
within the polygon. Gridcells partially inside the poly line
but with node point outside the poly line were not included,
and gridcells partially inside the poly line with node point
inside the poly line were counted as if the entire cell was
inside the poly line. Hence the local errors mostly cancelled
out.
The uncertainty in point elevations in the DEM is 0.3 m
(Geist and others, 2005). If the node elevations were linearly
distributed with respect to elevation, the uncertainty in area
in 100 m elevation bands would be 0.4%.
RESULTS
Ice flow in the southeast basin
Table 1. Stake velocity measurements on Engabreen in 2006, used
to define the ice drainage divide between Engabreen and
Storglombreen (Fig. 1). Directions are relative to north (=0), positive
towards west, negative towards east. There are missing values
where stakes were either melted out or not measured
28 June–3 Aug.
Stake
Northwest
North
Northeast
West
Middle
East
Southwest
South
Southeast
–1
ma
23
32
44
25
27
24
25
21
17
8
17
–9
–20
14
–3
–32
–17
–8
–4
3 Aug.–4 Oct.
–1
28 June–4 Oct.
8
m a–1
8
22
22
25
2
–30
5
25
30
25
–3
–24
8
22
25
27
20
–30
0
–6
–20
23
25
25
19
–31
–6
–6
–15
ma
The measured stake displacements range from 5 to 8 m, and
are equivalent to an annual speed of 19–30 m a–1 (Table 1).
Two of the stakes were not measured in October, and most
of the stakes were tilted due to melting. Hence, the October
measurements are probably less accurate than the August
measurements (which used the same base station) because it
is not entirely certain that the correct position was measured
for each stake. However, the original stake position was
clear in each case, and this has a minor effect on the results.
The three easternmost stakes, and to a lesser extent the three
middle stakes, all show a definite component of flow
eastwards. The displacement measurements show that ice
flow at this part of the hydrological drainage boundary is
from west to east; that is, ice that was previously considered
to be part of Engabreen actually flows east to Storglombreen.
This also agrees with the direction of ice flow shown by
interferometric synthetic aperture radar (InSAR) measurements of Svartisen from 1996 (T. Strozzi and others, http://
dib.joanneum.at/integral/results.html, Deliverable No. 8).
138
Elvehøy and others: Drainage boundaries and mass-balance results
Fig. 3. Area–altitude distributions (in 100 m elevation bins) from
three different drainage divides (Fig. 2) and a DEM from 30 June
2003.
The glaciological drainage basin
There are three areas where there is thought to be a large
discrepancy between ice drainage to the tongue of Engabreen and ice or water drainage to the lake Engabrevatnet.
1. The southeast basin. In the southeast basin close to
Snøtind the ice and water flux may contribute to either
Engabreen or Storglombreen. Based on the nine stake
velocities and the DEM from 30 June 2003, a drainage
divide in the southeast basin between ice draining
towards Engabreen and Storglombreen, respectively,
was defined. The new drainage divide is drawn manually
based on stake displacement directions. It is extrapolated
further uphill based on the DEM from 30 June 2003. This
area covers approximately 4.5 km2 above 1250 m a.s.l.
2. Litlebreen. The small outlet glacier Litlebreen (Fig. 2), the
northeastern part of the glacier area within the catchment
to Engabrevatnet, does not contribute ice to the terminus
of Engabreen. This area is 1.7 km2 and lies between 870
and 1205 m a.s.l. The drainage divide between Engabreen and Litlebreen was drawn normal to the contour
lines from the eastern end of the peak Møsbrømtuva.
3. The southwestern area. The southwestern part of the
catchment to Engabrevatnet is partly separated from the
glacier tongue by a cliff band. Some avalanching onto
the main glacier occurs, but the contribution of ice
seems small. The drainage divide is drawn from the
uppermost rock outcrop on the western side, uphill
normal to the contour lines. This area covers 3.8 km2
Table 2. Mean specific balances for Engabreen in m w.e. for 1970–
2006
Balance
Water drainage to
Engabrevatnet
(39.6 km2)
Ice drainage to
Engabrevatnet
(38.0 km2)
Ice drainage to
Engabreen tongue
(27.2 km2)
Winter
Summer
Net
2.92
–2.32
0.59
2.92
–2.34
0.58
2.80
–2.47
0.32
Fig. 4. Cumulative net mass balance at Engabreen, 1970–2006,
calculated from annual altitudinal net mass-balance curves and
altitudinal area distribution curves from three different glacier
drainage divides.
between 950 and 1360 m a.s.l. The exact location of this
boundary is somewhat subjective, but there is an area of
at least a few km2 that contributes water to Engabrevatnet
but only small ice volumes to the glacier tongue.
The area defined by ice drainage to the tongue of Engabreen
(27.2 km2) is considerably smaller than the two areas
defined by drainage to Engabrevatnet (38.0 and 39.6 km2).
The drainage area defined by ice flow to Engabreen does not
include areas around Snøtind (1594 m a.s.l.), the highest
peak on Vestisen. Consequently, the maximum elevation of
this drainage area is more than 100 m lower than the other
two drainage areas.
Altitudinal area distribution
The altitudinal area distributions (in %) for 100 m elevation
bands reveal that the ice drainage basin to Engabreen has a
considerably smaller portion of its area between 1300 and
1500 m a.s.l. than the other two drainage areas, and has a
larger portion of its area below 1100 m a.s.l. (Fig. 3).
Generally, the glacier area draining ice to the tongue of
Engabreen is topographically lower than the glacier area
draining water to Engabrevatnet.
Calculated mass balance
The annual mean specific winter and summer balance is
calculated from specific winter and summer net balance
curves and the three different altitudinal area distributions.
The spatial variations in winter and summer balance are not
evaluated, and the balance curves are used as they have
been reported to the WGMS. Mean values for 37 years are
shown in Table 2. A major conclusion is that the glacier
defined by ice flow to the terminus has a smaller winter
balance and a more negative summer balance than the other
two distributions. The difference in mean glacier-averaged
specific winter balance is –0.12 m w.e. (from 2.92 to
2.80 m w.e.), and in mean glacier-averaged specific summer
balance is –0.15 m w.e. (from –2.32 to –2.47 m w.e.). The
difference in mean net balance for the period 1970–2006 is
0.27 m w.e. (between +0.59 and +0.32 m w.e.). The cumulative mean specific net balance calculated with the three
different area–elevation distributions is shown in Figure 4.
The difference in cumulative mean specific mass balance
Elvehøy and others: Drainage boundaries and mass-balance results
139
between the calculations based on the two distributions
defined by Engabrevatnet is small. The mass balance
calculated using the area–elevation distribution defined by
ice flow to Engabreen is considerably less positive.
The difference in mean specific winter, summer and net
mass balance between the two drainage divides defined by
ice or water drainage to Engabrevatnet is <0.05 m w.e. The
difference between calculated mean specific mass balance
based on water discharge to Engabrevatnet and ice discharge to the tongue of Engabreen is larger. The maximum
difference between mean specific winter and summer
balance calculated for a single year is –0.26 m w.e. in
1989 and –0.27 m w.e. in 1990, respectively, while the
maximum difference in net balance is –0.40 m w.e. in 1989
and 1990. The difference in cumulative net balance for the
period 1970–2006 is –10 m w.e., which is almost half of the
calculated mass surplus in this period (Fig. 4).
The 2006 summer balance volume below 500 m a.s.l.
was calculated for the tongue as mapped in 1968 and in
2001. The area was 0.13 km2 larger in 2001 than in 1968,
and the glacier was 110 m more advanced in 2001 than in
1968. The summer balance volumes were calculated from
the specific summer balance curve (2006) and area–
elevation distributions from 1968 and 2001. The difference
in calculated specific summer mass balance based on
hydrological drainage divide to a slightly smaller and
steeper tongue in 1968 was 0.02 m w.e. The difference
between the reported specific summer balance based on
hydrological drainage divide and the specific summer
balance based on the ‘ice drainage to the glacier tongue’
divide is –0.20 m w.e. This shows that at Engabreen the
influence on the mass balance from moderate front position
variations is insignificant compared with the effects of the
choice of drainage divides.
DISCUSSION
CONCLUSIONS
Hydrological vs glaciological glacier
We have shown that the way the drainage divide is defined
can have a significant effect on the calculated specific mass
balance of a glacier. For Engabreen there are substantial
parts of the glacier where meltwater from the ice there drains
to Engabrevatnet, but where the ice does not flow and
contribute to the tongue of Engabreen. Three main areas of
Engabreen are identified here: one on the plateau where the
glaciological boundary or ice-flow perimeter can be defined
only by studying ice flow and may vary temporally; one
small outlet of Svartisen that is adjacent to Engabreen but
distinct from it; and an area above a cliff where there is only
limited ice avalanching down onto the main glacier body.
When the glacier is redefined according to a glaciological
instead of hydrological definition, not only is the area
changed substantially, but also the altitudinal area distribution. The ‘glaciological’ glacier has a smaller range in
elevation, the altitudinal interval containing the greatest area
of the glacier is lower (instead of 1300–1400 m a.s.l.
containing the greatest proportion at 25%, the elevation
bin 1200–1300 m a.s.l. contains the greatest proportion at
26%) and the glacier generally has a lower mean elevation.
This has important implications, such as in modelling glacier
response to climate change, especially for a maritime glacier
such as Engabreen that is sensitive to small changes in
temperature.
In this study, the drainage divides are drawn manually
from interpolated contour lines. The interpolations are thus
somewhat subjective. However, the varying shape of the
glacier surface on the plateau, and uncertainty and errors in
the bed and surface topography DEMs, mean that searching
for the ‘correct’ divide is probably futile. For Engabreen, the
differences in area because of these factors are insignificant
compared with the difference in area due to choice of
drainage divide.
Influence of front position variations
The influence of front position variations on mass-balance
results was compared with the influence of different choice
of drainage divides. Changes in front position are reported to
the WGMS every year, and changes in front position or
glacier length are often the parameter modelled when
studying glacier changes.
For plateau glaciers and ice caps, the spatial difference
between the ice-flow perimeter and the hydrological divide
can be significant. It is important that divides are defined
according to the assignment. When mass-balance and
glacier length changes are analyzed, the ice drainage to
the glacier tongue must be used, whereas studies of mass
balance and run-off must be based on water-drainage
divides. The example given here for Engabreen shows three
ways in which different parts of a glacier may ‘belong’ to that
glacier for hydrological purposes but not for ice-flow
purposes. On the plateau area of western Svartisen, ice
flow is slow and sub-parallel to the boundary between two
outlet glaciers. The ice here was previously thought to flow
towards Engabreen tongue, but precise stake position
measurements reveal that it actually flows toward Storglombreen. A small separate glacier tongue (Litlebreen)
terminates >1 km above the main glacier tongue of Engabreen. Water flow from both has the same eventual
destination but not the ice. Finally, ice on a steep slope
above the main glacier tongue contributes meltwater to
Engabreen that flows underneath the tongue, but the ice
rarely falls onto the tongue. Similar circumstances to these
three examples are regularly found on other glaciers.
A large proportion of the mass-balance glaciers in Norway
are outlets from ice caps. Another example where the
difference between area draining ice to the tongue and area
draining water to a lake or gauging station is significant is
Nigardsbreen, one of the major outlet glaciers from
Jostedalsbreen ice cap, the largest ice mass in mainland
Europe. At Nigardsbreen the difference in area is probably
around 15%. At Langfjordjøkelen in Finnmark, the northernmost glacier included in the mass-balance programme, there
are probably discrepancies between hydrological and glaciological drainage divides, too. This issue is significant in
regions where only a portion of a glacier body is monitored,
such as Svalbard, Iceland, Arctic Canada and Patagonia.
It is also relevant for valley and cirque glaciers where
parts of the glacier do not contribute glacier ice to the main
terminus, as is the case, for example, at Storbreen in Norway
and Vernagtferner in Austria. For researchers working on
glaciers where this issue is relevant, the most important step
is being aware of the problem and using caution and
precision in how different parameters are defined. Measurements of subglacial topography are essential in defining the
140
hydrological boundary for the glacier. To define the ice-flow
perimeter, measurements of ice motion are essential. It
should always be made clear whether the glacier boundary
defined is the hydrological boundary or the ice-flow
perimeter.
ACKNOWLEDGEMENTS
We are grateful to R. Engeset for initiating and supporting
this work, which is the first step to homogenize and improve
the quality and homogenization of NVE’s mass-balance
series. Many present and former colleagues at NVE have
contributed to the mass-balance fieldwork at Engabreen.
Reviews by P. Jansson and R. Pettersson improved the paper.
The mass-balance measurements at Engabreen are financed
by Statkraft Energi AS.
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